#4762 ⟨a, b | abaaaaba=aab⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba⁴ba = a²b and a ⋅ ab = a²b, however ba⁴ba ≠ ab

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = ab
2. d = aaac
Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(c) = deg(a) = 1, c < a; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaaaaba=aab d/ca/b ab=c,aaac=d morph:2/1,4/0
dc=cdddddddd
dda=ad
ac=cda
cdadada=d
db=ccdadadddddddddddddd
ab=c